📌 About the Project

The goal is to explore all possible combinations that could lead to the maximum product of three integers. This includes:

• The three largest positive numbers.
• The two most negative numbers multiplied by the largest positive number.

The algorithm avoids sorting for performance and instead uses manual tracking of max/min values.

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⚙️ System Workflow

🔁 Iterative Flow

1. Loop through the list once.
2. Track the top 3 max numbers (max1, max2, max3).
3. Track the bottom 2 min numbers (min1, min2).
4. Compare the product of:
   • max1 * max2 * max3
   • min1 * min2 * max1
5. Return the greater value.

🔁 Recursive Flow

• A recursive version applies the same logic but passes updated variables with each call.

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🗃️ Project Files Overview

File Name	Description
Code.py	Main iterative version of the algorithm. Efficient and avoids sorting.
Recursive_Code.py	Alternative recursive approach to calculate the result.
Main.py	Pseudocode-style breakdown of the logic used in the recursive algorithm.
Pseudocode.md	Logical flow documentation of the solution, useful for reports/presentation.

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🧪 Sample Input & Output

arr = [-10, -3, 5, 6, -20]
print(max_product_of_three(arr))  
# Output: 1200  → (-10 * -20 * 6)

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🧠 Key Features

• 🧮 Handles both negative and positive numbers.
• 🚀 Runs in linear time: O(n)
• 📦 No external libraries needed.
• 🔀 Includes both iterative and recursive implementations.

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🛠️ How to Run the Project

1. Install Python 3.x on your system.
2. Clone or download the project files.
3. Place all files in a single directory.
4. Run the main version using:

python Code.py

Or test the recursive version:

python Recursive_Code.py

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👨‍💻 Team Members

Project Leader: Amr Yasser Badr

Team Members:

• Youssef Mahmoud Younes
• Sama Saeed El-Fishawy